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Understanding the definition of a commutative algebra
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Hi, according to Eisenbud a commutative algebra over a commutative ring R is a commutative ring S with a ring homomorphism R-->S. In the case where R is a field we have that this homomorphism is necessarily injective when the map is non-trivial; however this doesn't hold for general commutative rings. So what's the deal here? Can you have a commutative algebra where the base ring doesn't inject itself inside the algebra?
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